<PAGE>
 
                                                                    EXHIBIT 10.2
                                                                                
                         REGISTRATION RIGHTS AGREEMENT
                         -----------------------------

     THIS AGREEMENT is made as of April 27, 1999, between CORE, INC., a
Massachusetts corporation (the "Company"), and Fleet National Bank, a national
banking association ("Purchaser").

     As an inducement to and in consideration of the execution and delivery by
Purchaser of the Third Amendment to Credit Agreement dated April 27, 1999
between the Company and the Purchaser (the "Third Amendment Agreement"), the
Company hereby covenants and agrees with the Purchaser and with each permitted
transferee of any of the Purchaser's Registrable Securities (as such term is
defined herein), as follows:
 
     1.   Demand Registration.
          ------------------- 

          (a)  Requests for Registration. Commencing one year after the 
               -------------------------
execution of this Agreement and during the term of this Agreement, the holders
of at least 50% of the Registrable Securities may request registration under the
Securities Act of all or part of their Registrable Securities on Form S-3 or any
similar or successor short-form registration statement (a "Short-Form
Registration"), provided that the Company shall be eligible to effect a Short-
Form Registration at the time such request is made. Within twenty business days
after receipt of any such request, the Company will give written notice of such
requested registration to all other holders of Registrable Securities and will
include in such registration all Registrable Securities with respect to which
the Company has received written requests for inclusion therein within 15 days
after the receipt of the Company's notice. A registration requested pursuant to
this paragraph 1(a) is referred to herein as a "Demand Registration".
Notwithstanding the foregoing, the Company shall not be required to effect any
Demand Registration if the aggregate number of shares of Registrable Securities
to be included therein (after giving effect to the requests of all holders of
the Company's securities to have securities included therein) shall be less than
50,000. Any holder of Registrable Securities who does not participate in a
Demand Registration shall have no further rights under paragraph 1 of this
Agreement, unless such Demand Registration does not count as a Short-Form
Registration, in which event such nonparticipating holder shall retain all of
such holder's rights under Section 1 of this Agreement with respect to all
subsequent Demand Registrations. A registration will not count as a Short-Form
Registration until it has become and remained (in accordance with paragraph 4(b)
below) effective, or if such registration has been withdrawn or discontinued at
the request of holders holding more than 50% of the Registrable Securities to be
included, or which have been included but remain unsold, in such registration.

          (b)  Demand Registration Expenses. The Company shall pay all 
               ----------------------------     
Registration Expenses (as defined in paragraph 5 below) for the Demand
Registration. The Demand Registration shall be an underwritten offering if the
Company or the holders of a majority of the Registrable Securities to be
included therein so request. Subject to paragraph 1(c) below, all costs of sale
and distribution of the registered shares shall be borne by the holders of
Registrable Securities participating in the offering.
<PAGE>

     (c)  Priority on Demand Registration.  If a Demand Registration is an
          -------------------------------
underwritten offering, and the managing underwriters advise the Company or the
holders of Registrable Securities included in such offering in writing that in
such managing underwriter's opinion the number of Registrable Securities and
other securities requested to be included exceeds the number of Registrable
Securities and other securities which can be sold in such offering without
adversely affecting the marketability of the offering, the Company will include
in such registration prior to the inclusion of any securities which are not
Registrable Securities the number of Registrable Securities requested to be
included which in the opinion of such underwriters can be sold, pro rata among
the respective holders on the basis of the amount of Registrable Securities
owned.

     (d)  Restrictions.  If, at the time of any request to register Registrable
          ------------                                                         
Securities pursuant to this paragraph 1, the Company

          (i)    has filed, or has definite and good faith plans to file within
90 days after the time of the request, a registered public offering as to which
the holders will be entitled to include Registrable Securities pursuant to
paragraph 2, or

          (ii)   is engaged in any other activity which, in the good faith
determination of the Company's board of directors, would be adversely affected
by the requested registration to the material detriment of the Company,

then the Company's board of directors may at its option direct that such request
be delayed for a period not in excess of six (6) months from the effective date
of such offering or the date of commencement of such other activity, as the case
may be.

     (e)  Selection of Underwriters.  In the Demand Registration, the Company 
          -------------------------   
will have the right to select the investment banker(s) and manager(s) to
administer the offering, subject to the approval of holders of a majority of the
Registrable Securities included in the Demand Registration, which approval will
not be unreasonably withheld.

     (f)  Underwriting Agreement. If requested by the underwriters for any
          ----------------------                                          
underwritten offering by holders of Registrable Securities pursuant to a
registration requested under this paragraph 1, the Company will enter into an
underwriting agreement with such underwriters for such offering, such agreement
to contain such representations and warranties by the Company and such other
terms and provisions as are customarily contained in agreements of that type,
including without limitation indemnities to the effect and to the extent
provided in paragraph 6 hereof.

     2.   Piggyback Registrations.
          ----------------------- 

     (a)  Right to Piggyback. Whenever the Company proposes to register any of 
          ------------------ 
its securities under the Securities Act of 1933 (the "Securities Act") and the
registration form to be used may be used for the registration of Registrable
Securities (each a "Piggyback Registration"), the Company will give prompt
written notice to all holders of Registrable Securities of its intention to
effect such a registration and will include in such registration all Registrable
Securities with 
 
                                       2
<PAGE>
 
respect to which the Company has received written requests for inclusion therein
within 15 days after the receipt of the Company's notice.

     (b)  Piggyback Expenses. The Registration Expenses of the holders of
          ------------------                                             
Registrable Securities will be paid by the Company in all Piggyback
Registrations.

     (c)  Priority on Primary Registrations. If a Piggyback Registration is an
          ---------------------------------                                   
underwritten primary registration on behalf of the Company, and the managing
underwriters advise the Company in writing that in their opinion the number of
securities requested to be included in such registration exceeds the number
which can be sold in such offering without adversely affecting the marketability
of the offering, the Company will include in such registration (i) first, the
securities the Company proposes to sell, (ii) second, the Company's securities
issued to Transcend Services, Inc. in connection with the Company's acquisition
of all of the assets of Transcend Case Management, Inc. which shares are subject
to a Registration Rights Agreement entered into between the Company and
Transcend Services, Inc. on March 17, 1998 (the "Transcend Registrable
Securities") requested to be included in such registration, (iii) third, (A) the
securities, if any, requested to be registered under a Registration Rights
Agreement entered into between the Company and the Purchaser on August 31, 1998
(the "August 1998 Registrable Securities"), and (B) the Registrable Securities
requested to be included in such registration, pro rata among the holders of the
August 1998 Registrable Securities and the Registrable Securities on the basis
of the number of shares owned by each such holder, and (iv) fourth, other
securities requested to be included in such registration.

     (d)  Priority on Secondary Registrations. If a Piggyback Registration is an
          -----------------------------------                                   
underwritten secondary registration on behalf of holders of the Company's
securities, and the managing underwriters advise the Company in writing that in
their opinion the number of securities requested to be included in such
registration exceeds the number which can be sold in such offering without
adversely affecting the marketability of the offering, the Company will include
in such registration (i) first, the securities requested to be included therein
by the holders requesting such registration, (ii) the Transcend Registrable
Securities requested to be included, (iii) third, (A) the August 1998
Registrable Securities, and (B) the Registrable Securities requested to be
included in such registration, pro rata among the holders of the August 1998
Registrable Securities and the Registrable Securities on the basis of the number
of shares owned by each such holder, and (iv) fourth, other securities requested
to be included in such registration.

     (e)  Selection of Underwriters. If any Piggyback Registration is an
          -------------------------                                     
underwritten offering, the Company in its sole discretion shall select the
investment banker(s) and manager(s) for the offering.

     (f)  Underwriting Agreement. If requested by the underwriters for any
          ----------------------                                          
underwritten offering by holders of Registrable Securities pursuant to a
registration requested under this paragraph 2, the holders of Registrable
Securities participating in such registration shall enter into an underwriting
agreement with such underwriters for such offering, such agreement to contain
such representations and warranties by the Company and such other terms and
provisions as are customarily contained in agreements of that type, including
without limitation indemnities to the effect and to the extent provided in
paragraph 6 hereof.

                                       3
<PAGE>
 


                                       4
<PAGE>
 
     3.   Holdback.
          -------- 

     (a)  Each holder of Registrable Securities participating in a Demand
Registration or Piggyback Registration agrees not to effect any public sale or
distribution (including sales pursuant to Rule 144 or Rule 144A) of equity
securities of the Company, or any securities convertible into or exchangeable or
exercisable for such securities, during a period not exceeding the seven days
prior to and the 180-day period beginning on the effective date of any
underwritten Demand Registration or any underwritten Piggyback Registration in
which Registrable Securities of holder are included (except as part of such
underwritten registration), unless the underwriters managing the registered
public offering otherwise agree, provided that the holders shall not be subject
to a longer period than any other seller of securities included in such
offering.

     (b)  The 180-day period referred to in paragraph 3(a) above may be changed
unilaterally by the Company at the request of its investment banker and/or the
manager of the offering, provided, however that (i) such period shall not be
extended beyond 270 days and (ii) the holders shall not be subject to a longer
period than any other similarly situated Person.

     4.   Registration Procedures. Whenever the holders of Registrable 
          ----------------------- 
Securities have requested that any Registrable Securities be registered pursuant
to this Agreement, the Company will use its best efforts to effect the
registration and the sale of such Registrable Securities in accordance with the
intended method of disposition thereof, and pursuant thereto the Company will as
expeditiously as possible:

     (a)  prepare and file with the Securities and Exchange Commission (in the
case of a registration pursuant to paragraph 1 hereof, such filing to be made
within 30 days of the initial request therefor) a registration statement with
respect to such Registrable Securities and use its reasonable best efforts to
cause such registration statement to become and remain effective (provided that
not less than 5 business days before filing a registration statement or
prospectus or any amendments or supplements thereto, the Company will furnish to
the counsel selected by the holders of a majority of the Registrable Securities
covered by such registration statement copies of all such documents proposed to
be filed, which documents will be subject to the reasonable review of such
counsel);

     (b)  prepare and file with the Securities and Exchange Commission such
amendments and supplements to such registration statement and the prospectus
used in connection therewith as may be necessary to keep such registration
statement effective for a period of not less than six months and comply with the
provisions of the Securities Act with respect to the disposition of all
securities covered by such registration statement during such period in
accordance with the intended methods of disposition by the sellers thereof set
forth in such registration statement;

     (c)  furnish to each seller of Registrable Securities and each underwriter,
if any, of the securities being sold by such seller, such number of copies of
such registration statement, each amendment and supplement thereto, the
prospectus included in such registration statement (including each preliminary
prospectus) and such other documents as such seller may reasonably request in
order to facilitate the disposition of the Registrable Securities owned by such
seller;

                                       5
<PAGE>
 
     (d)  use its reasonable best efforts to register or qualify such
Registrable Securities under such other securities or blue sky laws of such
jurisdictions as any seller reasonably requests and do any and all other acts
and things which may be reasonably necessary or advisable to enable such seller
to consummate the disposition in such jurisdictions of the Registrable
Securities owned by such seller (provided that the Company will not be required
to (i) qualify generally to do business in any jurisdiction where it would not
otherwise be required to qualify but for this subparagraph, (ii) subject itself
to taxation in any such jurisdiction, or (iii) consent to general service of
process in any such jurisdiction);

     (e)  notify each seller of such Registrable Securities at any time when a
prospectus relating thereto is required to be delivered under the Securities
Act, of the happening of any event as a result of which the prospectus included
in such registration statement contains an untrue statement of a material fact
or omits any fact necessary to make the statements therein not misleading, and,
at the request of any such seller, the Company will prepare a supplement or
amendment to such prospectus so that, as thereafter delivered to the purchasers
of such Registrable Securities, such prospectus will not contain an untrue
statement of a material fact or omit to state any fact necessary to make the
statements therein not misleading;

     (f)  advise each seller of Registrable Securities covered by such
registration statement, promptly after it receives notice thereof, of the time
when such registration statement, or any supplement thereto, or any amendment to
such registration statement have become effective or any related prospectus or
any supplement to such prospectus or any amendment to such prospectus has been
filed, of the issuance by the Securities and Exchange Commission of any stop
order or of any order preventing or suspending the use of any related
preliminary prospectus or prospectus, of the suspension of the qualification of
such Registrable Securities for offering or sale in any jurisdiction, of the
initiation or threatening of any proceeding for any such purpose, or of any
request by the Securities and Exchange Commission for the amending or
supplementing of such registration statement or prospectus or for additional
information; and in the event of the issuance of any stop order or of any order
preventing or suspending the use of any such preliminary prospectus or
prospectus or suspending any such qualification, to use promptly its best
efforts to obtain withdrawal of such order;

     (g)  file promptly all documents required to be filed with the Securities
and Exchange Commission pursuant to Sections 13, 14 or 15(d) of the Exchange Act
subsequent to the time such registration statement becomes effective and during
any period when any related prospectus is required to be delivered;

     (h)  cause all such Registrable Securities to be listed on each securities
exchange on which similar securities issued by the Company are then listed and,
if not so listed, to be listed on the NASD Automated Quotation System if so
qualified;

     (i)  provide an independent transfer agent and registrar for all such
Registrable Securities not later than the effective date of such registration
statement;

     (j)  enter into such customary agreements (including underwriting
agreements in customary form) and take all such other actions as the holders of
a majority of the Registrable Securities 

                                       6
<PAGE>
 
being sold or the underwriters, if any, reasonably request in order to expedite
or facilitate the disposition of such Registrable Securities;

     (k)  make available for inspection by any seller of Registrable Securities,
any underwriter participating in any disposition pursuant to such registration
statement and any attorney, accountant or other agent retained by any such
seller or underwriter, all financial and other records, pertinent corporate
documents and properties of the Company, and cause the Company's officers,
directors, employees and independent accountants to supply all information
reasonably requested by any such seller, underwriter, attorney, accountant or
agent in connection with such registration statement; and

     (l)  otherwise use its best efforts to comply with all applicable rules and
regulations of the Securities and Exchange Commission, and make available to its
security holders, as soon as reasonably practicable, an earnings statement
covering the period of at least twelve months beginning with the first day of
the Company's first full calendar quarter after the effective date of the
registration statement, which earnings statement shall satisfy the provisions of
Section ll(a) of the Securities Act and Rule 158 thereunder.

     In connection with the Demand Registration or any Piggyback Registration,
the holders of Registrable Securities will expeditiously supply the Company with
all reasonably requested information and copies of all documents reasonably
necessary to effect such registration in compliance with the Securities Act and
the rules and regulations thereunder and shall otherwise cooperate with the
Company and its counsel in expediting the effectiveness of any such
registration.

     5.   Registration Expenses.
          --------------------- 

     (a)  All expenses incident to the Company's performance of or compliance
with this Agreement, including without limitation all registration and filing
fees, fees and expenses of compliance with securities or blue sky laws, printing
expenses, messenger and delivery expenses, and fees and disbursements of counsel
for the Company and all independent certified public accountants, underwriters
(excluding discounts and commissions and excluding legal fees and disbursements
of any counsel for the holders of Registrable Securities) and other Persons
retained by the Company (all such expenses being herein called "Registration
Expenses"), will be borne as provided in this Agreement, except that the Company
will, in any event, pay its internal expenses (including, without limitation,
all salaries and expenses of its officers and employees performing legal or
accounting duties), the expense of any annual audit or quarterly review, the
expense of any liability insurance and the expenses and fees for listing the
securities to be registered on each securities exchange on which similar
securities issued by the Company are then listed or on the NASD Automated
Quotation System.

     (b)  To the extent expenses in connection with a registration hereunder are
not required to be paid by the Company, each holder of securities included in
any registration hereunder will pay those Registration Expenses allocable to the
registration of such holder's securities so included, and any Registration
Expenses not so allocable will be borne by all sellers of securities included in
such registration in proportion to the aggregate selling price of the securities
to be so registered.

                                       7
<PAGE>

     6.   Indemnification.
          --------------- 

     (a)  The Company agrees to indemnify, to the extent permitted by law, each
holder of Registrable Securities participating in a Demand Registration or a
Piggyback Registration, such holder's officers, directors, counsel and each
Person who controls or is affiliated with such holder (within the meaning of the
Securities Act) against all losses, claims, damages, liabilities and expenses
resulting from any untrue or alleged untrue statement of material fact contained
in any registration statement, prospectus or preliminary prospectus or any
amendment thereof or supplement thereto or any omission or alleged omission of a
material fact required to be stated therein or necessary to make the statements
therein not misleading, except insofar as the same are caused by or contained in
any information furnished in writing to the Company by such holder expressly for
use therein or by such holder's failure to deliver a copy of the registration
statement or prospectus or any amendments or supplements thereto after the
Company has furnished such holder with a sufficient number of copies of the
same.  In connection with an underwritten offering, the Company will indemnify
such underwriters, their officers and directors and each Person who controls
such underwriters (within the meaning of the Securities Act) to the same extent
as provided above with respect to the indemnification of the holders; provided
that such underwriters indemnify the Company to the same extent as provided in
subparagraph (b) below with respect to indemnification of the Company by the
holders.

     (b)  In connection with any registration statement in which a holder of
Registrable Securities is participating, each such holder will furnish to the
Company in writing such information and affidavits as the Company reasonably
requests for use in connection with any such registration statement or
prospectus and, to the extent permitted by law, will indemnify the Company, its
directors, officers, counsel and each Person who controls the Company (within
the meaning of the Securities Act) against any losses, claims, damages,
liabilities and expenses resulting from any untrue or alleged untrue statement
of material fact contained in the registration statement, prospectus or
preliminary prospectus or any amendment thereof or supplement thereto or any
omission or alleged omission of a material fact required to be stated therein or
necessary to make the statements therein not misleading, but only to the extent
that such untrue statement or omission is contained in any information or
affidavit so furnished in writing by such holder; provided that the obligation
to indemnify will be individual to each holder and will be limited to the net
amount of proceeds received by such holder from the sale of Registrable
Securities pursuant to such registration statement.

     (c)  Any Person entitled to indemnification hereunder will (i) give prompt
written notice to the indemnifying party of any claim with respect to which it
seeks indemnification and (ii) unless in such indemnified party's reasonable
judgment a conflict of interest between such indemnified and indemnifying
parties may exist with respect to such claim, permit such indemnifying party to
assume the defense of such claim with counsel reasonably satisfactory to the
indemnified party. If such defense is assumed, the indemnifying party will not
be subject to any liability for any settlement made by the indemnified party
without its consent (but such consent will not be unreasonably withheld). An
indemnifying party who is not entitled to, or elects not to, assume the defense
of a claim will not be obligated to pay the fees and expenses of more than one
counsel for all parties indemnified by such indemnifying party with respect to
such claim, unless in the 

                                      8 
<PAGE>

reasonable judgment of any indemnified party a conflict of interest may exist
between such indemnified party and any other of such indemnified parties with
respect to such claim.

     (d)  The indemnification provided for under this Agreement will remain in
full force and effect regardless of any investigation made by or on behalf of
the indemnified party or any officer, director or controlling Person of such
indemnified party and will survive the transfer of securities. The Company also
agrees to make such provisions, as are reasonably requested by any indemnified
party, for contribution to such party in the event the Company's indemnification
is unavailable for any reason. No person guilty of fraudulent misrepresentation
(within the meaning of Section 11(f) of the Securities Act) shall be entitled to
contribution from any person who was not guilty of such fraudulent
misrepresentation.

     The indemnification and contribution required by this paragraph 6 shall be
made by periodic payments of the amount thereof during the course of the
investigation or defense, as and when bills are received or expense, loss,
damage or liability is incurred.

     7.   Participation in Underwritten Registrations. No Person may 
          -------------------------------------------   
participate in any registration hereunder which is underwritten unless such
Person (a) agrees to sell such Person's securities on the basis provided in any
underwriting arrangements approved by the Person or Persons entitled hereunder
to approve such arrangements and (b) completes and executes all questionnaires,
powers of attorney, indemnities, underwriting agreements and other documents
required under the terms of such underwriting arrangements all in accordance
with the other terms and conditions hereof.

     8.   Rule 144. The Company covenants that it will timely file the reports
          --------                                                            
required to be filed by it under the Securities Act or the Securities Exchange
Act of 1934, as from time to time in effect (the "Exchange Act"), including but
not limited to the reports under Sections 13 and 15(d) of the Exchange Act
referred to in subparagraph (c)(1) of Rule 144 adopted by the Securities and
Exchange Commission under the Securities Act, and the rules and regulations
adopted by the Securities and Exchange Commission thereunder, and will take such
further action as any holder of Registrable Securities may reasonably request,
all to the extent required from time to time to enable such holder to sell
Registrable Securities without registration under the Securities Act within the
limitation of the exemptions provided by (i) Rule 144 under the Securities Act,
as such Rule may be amended from time to time, or (ii) any similar rule or
regulation hereafter adopted by the Securities and Exchange Commission.  Upon
the request of any holder of Registrable Securities, the Company will deliver to
such holder a written statement as to whether it has complied with such
requirements.

     9.   Definitions.
          ----------- 
 
     "Person" means an individual, a partnership, a corporation, a limited
liability company, an association, a joint stock company, a trust, a joint
venture, an unincorporated organization and a governmental entity or any
department, agency or political subdivision thereof.

     "Registrable Securities" means any of the shares of the Company's common
stock which are issued upon exercise of the Warrant, including without
limitation any Common Stock issued  

                                       9
<PAGE>
 
or issuable pursuant to Section 2 thereof. As to any particular Registrable
Securities, such securities will cease to be Registrable Securities upon removal
of any restrictive legend therefrom upon shares becoming fully saleable under
Rule 144(k).

     "Registration Expenses" means as defined in paragraph 5(a) hereto.

     "Warrant" means the warrant for common stock issued to Purchaser by CORE,
INC. on April 27, 1999.

     Unless otherwise stated, other capitalized terms contained herein have the
meanings set forth in the Third Amendment Agreement.

     10.  Term.  This Agreement shall terminate upon the earliest of the 
          ---- 
following events: (i) June 30, 2004 (provided if the holders of Registrable
Securities have given notice of the exercise of their registration rights
hereunder prior to such date, the Company shall honor its obligation hereunder
after such date), (ii) upon all of the Registrable Securities being registered
and sold pursuant to an effective registration statement, or (iii) upon the sale
of all of the Registrable Securities through any combination of methods
including Rule 144 or Rule 144A.

     11.  Representations and Warranties of the Company.  The Company 
          ---------------------------------------------               
represents and warrants to Purchaser as follows:

     (a)  The execution, delivery and performance of this Registration Rights
Agreement by the Company have been duly authorized by all requisite corporate
action and will not violate any provision of law, any order of any court or
other agency of government, the Articles of Organization or By-laws of the
Company, or any provision of any indenture, agreement or other instrument to
which it or any of its properties or assets is bound, or a default under any
such indenture, agreement or other instrument, or result in the creation or
imposition of any lien, charge or encumbrance of any nature whatsoever upon any
properties or assets of the Company.

     (b)  This Agreement has been duly executed and delivered by the Company and
constitutes the legal, valid and binding obligation of the Company, enforceable
in accordance with its terms, subject, as to enforcement of remedies, to
applicable bankruptcy, insolvency, moratorium and other similar laws and to
general principles of equity, and except as rights to indemnity or contribution
hereunder may be limited by public policy or by law.

     12.  Miscellaneous.
          ------------- 

     (a)  No Inconsistent Agreements. The Company will not hereafter enter 
          --------------------------
into any agreement with respect to its securities which is inconsistent with or
violates the rights granted to the holders of Registrable Securities in this
Agreement. The Purchaser acknowledges that it is aware of, has received a copy
of and reviewed the Registration Rights Agreement between the Company and
Transcend Services, Inc. dated March 17, 1998, the Registration Rights Agreement
between the Company and five stockholders dated August 31, 1998 and the
Registration Rights Agreement between the Company and the Purchaser dated August
31, 1998.

                                       10
<PAGE>
 
     (b)  Adjustments Affecting Registrable Securities. The Company will not 
          --------------------------------------------
take any action, or permit any change to occur, with respect to its securities
which would adversely affect the ability of the holders of Registrable
Securities to include such Registrable Securities in a registration undertaken
pursuant to this Agreement or which would materially adversely affect the
marketability of such Registrable Securities in any such registration
(including, without limitation, effecting a stock split or a combination of
shares).

     (c)  Specific Performance.  Each of the parties hereto acknowledges and
          --------------------                                              
agrees that the other Parties hereto would be damaged irreparably in the event
any of the provisions of this Agreement are not performed in accordance with
their specific terms or otherwise are breached. Accordingly, each of the parties
hereto agrees that each other party hereto shall be entitled to an injunction or
injunctions to prevent breaches of the provisions of this Agreement and to
enforce specifically this Agreement and the terms and provisions hereof in any
action instituted in any court of the United States or any state thereof having
jurisdiction over the parties hereto and the matter in addition to any other
remedy to which it may be entitled, at law or in equity.

     (d)  Amendments and Waivers. Except as otherwise provided herein, the
          ----------------------                                          
provisions of this Agreement may be amended or waived only upon the prior
written consent of the Company and holders of at least a majority of the
Registrable Securities.

     (e)  Successors and Assigns. All covenants and agreements in this 
          ----------------------                  
Agreement by or on behalf of any of the parties hereto will bind and inure to
the benefit of the respective successors and assigns of the parties hereto
whether so expressed or not. Purchaser and its assigns shall not be permitted to
assign their respective rights under this Agreement to any party without the
Company's prior written consent, which consent shall not be unreasonably
withheld, provided however the Company hereby consents to assignment of rights
hereunder to the following permitted transferees: any affiliate of Fleet
National Bank or any successor of Fleet National Bank or affiliates thereof.

     (f)  Severability. Whenever possible, each provision of this Agreement 
          ------------   
will be interpreted in such manner as to be effective and valid under applicable
law, but if any provision of this Agreement is held to be prohibited by or
invalid under applicable law, such provision will be ineffective only to the
extent of such prohibition or invalidity, without invalidating the remainder of
this Agreement.

     (g)  Counterparts. This Agreement may be executed simultaneously in two 
          ------------      
or more counterparts, any one of which need not contain the signatures of more
than one party, but all such counterparts taken together will constitute one and
the same Agreement.

     (h)  Descriptive Headings. The descriptive headings of this Agreement are
          --------------------                                                
inserted for convenience only and do not constitute a part of this Agreement.

     (i)  Governing Law. The corporate law of Massachusetts will govern all 
          -------------      
issues concerning the relative rights of the Company and its stockholders. All
other questions concerning the construction, validity and interpretation of this
Agreement and the exhibits and schedules hereto will be governed by the internal
law, and not the law of conflicts, of Massachusetts.

                                       11
<PAGE>
 
     (j)  Notices. All notices, demands or other communications to be given or
          -------                                                             
delivered under or by reason of the provisions of this Agreement shall be in
writing and shall be deemed to have been given when delivered personally to the
recipient, sent to the recipient by reputable express courier service (charges
prepaid) or mailed to the recipient by certified or registered mail, return
receipt requested and postage prepaid. Such notices, demands and other
communications will be sent to Purchaser or its assigns at the address indicated
in the Credit Agreement, or to such other address or to the attention of such
other person as the recipient party has specified by prior written notice to the
sending party.

     (k)  Entire Agreement. This Agreement constitutes the entire understanding 
          ----------------        
of the parties hereto with respect to the subject matter hereof and supersedes
any and all prior understandings and agreements, whether written or oral, with
respect to such subject matter.

                          [SIGNATURES ON FOLLOWING PAGE]

                                       12
<PAGE>

     IN WITNESS WHEREOF, the parties have executed this Agreement as of the date
first written above.


                                  CORE, INC.                         
                                                                         
                                                                         
                                  By: /s/ William E. Nixon           
                                      -----------------------------------------
                                      William E. Nixon, Chief Financial Officer 
                                                                         
                                                                         
                                  PURCHASER                          
                                                                         
                                  FLEET NATIONAL BANK                
                                                                         
                                                                         
                                  By: /s/ Jeffrey A. Simpson         
                                      -----------------------------------------
                                  Title:  Vice President